Resonance phenomena simulated by finite differences and biased noise inputs

In Lecture-21.nb, a second-order differencing scheme that iteratively solved y'' + βy' + γy=0 with the specification of two initial values.

Modify this to add a little random noise to y[i] at each step and observe how this behaves---this version will store the noise added at each iteration so that it can be visualized later....

Setting up a function that takes particular parameters and a "noise amplitude" of

Now suppose there is a periodic bias that tends to kick the displacement one direction more than the other:

Generate the data set---this takes quite a while